LMFDB - Embedded newform 322.2.a.f.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [322,2,Mod(1,322)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(322, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("322.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 322 = 2 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	322.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$2.57118294509$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{12})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 3 $ x^2 - 3
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.73205$ of defining polynomial
Character	$\chi$	$=$	322.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +0.732051 q^{3} +1.00000 q^{4} +2.73205 q^{5} +0.732051 q^{6} +1.00000 q^{7} +1.00000 q^{8} -2.46410 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.732051 q^{3} +1.00000 q^{4} +2.73205 q^{5} +0.732051 q^{6} +1.00000 q^{7} +1.00000 q^{8} -2.46410 q^{9} +2.73205 q^{10} -3.46410 q^{11} +0.732051 q^{12} -1.46410 q^{13} +1.00000 q^{14} +2.00000 q^{15} +1.00000 q^{16} -0.732051 q^{17} -2.46410 q^{18} -2.00000 q^{19} +2.73205 q^{20} +0.732051 q^{21} -3.46410 q^{22} +1.00000 q^{23} +0.732051 q^{24} +2.46410 q^{25} -1.46410 q^{26} -4.00000 q^{27} +1.00000 q^{28} +8.00000 q^{29} +2.00000 q^{30} +0.196152 q^{31} +1.00000 q^{32} -2.53590 q^{33} -0.732051 q^{34} +2.73205 q^{35} -2.46410 q^{36} +0.535898 q^{37} -2.00000 q^{38} -1.07180 q^{39} +2.73205 q^{40} -2.00000 q^{41} +0.732051 q^{42} -3.46410 q^{44} -6.73205 q^{45} +1.00000 q^{46} -8.19615 q^{47} +0.732051 q^{48} +1.00000 q^{49} +2.46410 q^{50} -0.535898 q^{51} -1.46410 q^{52} +3.46410 q^{53} -4.00000 q^{54} -9.46410 q^{55} +1.00000 q^{56} -1.46410 q^{57} +8.00000 q^{58} -11.6603 q^{59} +2.00000 q^{60} +8.19615 q^{61} +0.196152 q^{62} -2.46410 q^{63} +1.00000 q^{64} -4.00000 q^{65} -2.53590 q^{66} -4.53590 q^{67} -0.732051 q^{68} +0.732051 q^{69} +2.73205 q^{70} +8.39230 q^{71} -2.46410 q^{72} -7.46410 q^{73} +0.535898 q^{74} +1.80385 q^{75} -2.00000 q^{76} -3.46410 q^{77} -1.07180 q^{78} +0.928203 q^{79} +2.73205 q^{80} +4.46410 q^{81} -2.00000 q^{82} -6.39230 q^{83} +0.732051 q^{84} -2.00000 q^{85} +5.85641 q^{87} -3.46410 q^{88} +14.1962 q^{89} -6.73205 q^{90} -1.46410 q^{91} +1.00000 q^{92} +0.143594 q^{93} -8.19615 q^{94} -5.46410 q^{95} +0.732051 q^{96} -8.73205 q^{97} +1.00000 q^{98} +8.53590 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{6} + 2 q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 - 2 * q^6 + 2 * q^7 + 2 * q^8 + 2 * q^9	$ 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{6} + 2 q^{7} + 2 q^{8} + 2 q^{9} + 2 q^{10} - 2 q^{12} + 4 q^{13} + 2 q^{14} + 4 q^{15} + 2 q^{16} + 2 q^{17} + 2 q^{18} - 4 q^{19} + 2 q^{20} - 2 q^{21} + 2 q^{23} - 2 q^{24} - 2 q^{25} + 4 q^{26} - 8 q^{27} + 2 q^{28} + 16 q^{29} + 4 q^{30} - 10 q^{31} + 2 q^{32} - 12 q^{33} + 2 q^{34} + 2 q^{35} + 2 q^{36} + 8 q^{37} - 4 q^{38} - 16 q^{39} + 2 q^{40} - 4 q^{41} - 2 q^{42} - 10 q^{45} + 2 q^{46} - 6 q^{47} - 2 q^{48} + 2 q^{49} - 2 q^{50} - 8 q^{51} + 4 q^{52} - 8 q^{54} - 12 q^{55} + 2 q^{56} + 4 q^{57} + 16 q^{58} - 6 q^{59} + 4 q^{60} + 6 q^{61} - 10 q^{62} + 2 q^{63} + 2 q^{64} - 8 q^{65} - 12 q^{66} - 16 q^{67} + 2 q^{68} - 2 q^{69} + 2 q^{70} - 4 q^{71} + 2 q^{72} - 8 q^{73} + 8 q^{74} + 14 q^{75} - 4 q^{76} - 16 q^{78} - 12 q^{79} + 2 q^{80} + 2 q^{81} - 4 q^{82} + 8 q^{83} - 2 q^{84} - 4 q^{85} - 16 q^{87} + 18 q^{89} - 10 q^{90} + 4 q^{91} + 2 q^{92} + 28 q^{93} - 6 q^{94} - 4 q^{95} - 2 q^{96} - 14 q^{97} + 2 q^{98} + 24 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 - 2 * q^6 + 2 * q^7 + 2 * q^8 + 2 * q^9 + 2 * q^10 - 2 * q^12 + 4 * q^13 + 2 * q^14 + 4 * q^15 + 2 * q^16 + 2 * q^17 + 2 * q^18 - 4 * q^19 + 2 * q^20 - 2 * q^21 + 2 * q^23 - 2 * q^24 - 2 * q^25 + 4 * q^26 - 8 * q^27 + 2 * q^28 + 16 * q^29 + 4 * q^30 - 10 * q^31 + 2 * q^32 - 12 * q^33 + 2 * q^34 + 2 * q^35 + 2 * q^36 + 8 * q^37 - 4 * q^38 - 16 * q^39 + 2 * q^40 - 4 * q^41 - 2 * q^42 - 10 * q^45 + 2 * q^46 - 6 * q^47 - 2 * q^48 + 2 * q^49 - 2 * q^50 - 8 * q^51 + 4 * q^52 - 8 * q^54 - 12 * q^55 + 2 * q^56 + 4 * q^57 + 16 * q^58 - 6 * q^59 + 4 * q^60 + 6 * q^61 - 10 * q^62 + 2 * q^63 + 2 * q^64 - 8 * q^65 - 12 * q^66 - 16 * q^67 + 2 * q^68 - 2 * q^69 + 2 * q^70 - 4 * q^71 + 2 * q^72 - 8 * q^73 + 8 * q^74 + 14 * q^75 - 4 * q^76 - 16 * q^78 - 12 * q^79 + 2 * q^80 + 2 * q^81 - 4 * q^82 + 8 * q^83 - 2 * q^84 - 4 * q^85 - 16 * q^87 + 18 * q^89 - 10 * q^90 + 4 * q^91 + 2 * q^92 + 28 * q^93 - 6 * q^94 - 4 * q^95 - 2 * q^96 - 14 * q^97 + 2 * q^98 + 24 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	0.732051	0.422650	0.211325	−	0.977416i	$-0.432222\pi$
$3$	0.732051	0.422650	0.211325	+	0.977416i	$0.432222\pi$
$4$	1.00000	0.500000
$5$	2.73205	1.22181	0.610905	−	0.791704i	$-0.290806\pi$
$5$	2.73205	1.22181	0.610905	+	0.791704i	$0.290806\pi$
$6$	0.732051	0.298858
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	−2.46410	−0.821367
$10$	2.73205	0.863950
$11$	−3.46410	−1.04447	−0.522233	−	0.852803i	$-0.674901\pi$
$11$	−3.46410	−1.04447	−0.522233	+	0.852803i	$0.674901\pi$
$12$	0.732051	0.211325
$13$	−1.46410	−0.406069	−0.203034	−	0.979172i	$-0.565080\pi$
$13$	−1.46410	−0.406069	−0.203034	+	0.979172i	$0.565080\pi$
$14$	1.00000	0.267261
$15$	2.00000	0.516398
$16$	1.00000	0.250000
$17$	−0.732051	−0.177548	−0.0887742	−	0.996052i	$-0.528295\pi$
$17$	−0.732051	−0.177548	−0.0887742	+	0.996052i	$0.528295\pi$
$18$	−2.46410	−0.580794
$19$	−2.00000	−0.458831	−0.229416	−	0.973329i	$-0.573682\pi$
$19$	−2.00000	−0.458831	−0.229416	+	0.973329i	$0.573682\pi$
$20$	2.73205	0.610905
$21$	0.732051	0.159747
$22$	−3.46410	−0.738549
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	0.732051	0.149429
$25$	2.46410	0.492820
$26$	−1.46410	−0.287134
$27$	−4.00000	−0.769800
$28$	1.00000	0.188982
$29$	8.00000	1.48556	0.742781	−	0.669534i	$-0.233506\pi$
$29$	8.00000	1.48556	0.742781	+	0.669534i	$0.233506\pi$
$30$	2.00000	0.365148
$31$	0.196152	0.0352300	0.0176150	−	0.999845i	$-0.494393\pi$
$31$	0.196152	0.0352300	0.0176150	+	0.999845i	$0.494393\pi$
$32$	1.00000	0.176777
$33$	−2.53590	−0.441443
$34$	−0.732051	−0.125546
$35$	2.73205	0.461801
$36$	−2.46410	−0.410684
$37$	0.535898	0.0881012	0.0440506	−	0.999029i	$-0.485974\pi$
$37$	0.535898	0.0881012	0.0440506	+	0.999029i	$0.485974\pi$
$38$	−2.00000	−0.324443
$39$	−1.07180	−0.171625
$40$	2.73205	0.431975
$41$	−2.00000	−0.312348	−0.156174	−	0.987730i	$-0.549916\pi$
$41$	−2.00000	−0.312348	−0.156174	+	0.987730i	$0.549916\pi$
$42$	0.732051	0.112958
$43$	0	0		−	1.00000i	$-0.5\pi$
$43$	0	0			1.00000i	$0.5\pi$
$44$	−3.46410	−0.522233
$45$	−6.73205	−1.00355
$46$	1.00000	0.147442
$47$	−8.19615	−1.19553	−0.597766	−	0.801671i	$-0.703945\pi$
$47$	−8.19615	−1.19553	−0.597766	+	0.801671i	$0.703945\pi$
$48$	0.732051	0.105662
$49$	1.00000	0.142857
$50$	2.46410	0.348477
$51$	−0.535898	−0.0750408
$52$	−1.46410	−0.203034
$53$	3.46410	0.475831	0.237915	−	0.971286i	$-0.423536\pi$
$53$	3.46410	0.475831	0.237915	+	0.971286i	$0.423536\pi$
$54$	−4.00000	−0.544331
$55$	−9.46410	−1.27614
$56$	1.00000	0.133631
$57$	−1.46410	−0.193925
$58$	8.00000	1.05045
$59$	−11.6603	−1.51804	−0.759018	−	0.651070i	$-0.774321\pi$
$59$	−11.6603	−1.51804	−0.759018	+	0.651070i	$0.774321\pi$
$60$	2.00000	0.258199
$61$	8.19615	1.04941	0.524705	−	0.851284i	$-0.324176\pi$
$61$	8.19615	1.04941	0.524705	+	0.851284i	$0.324176\pi$
$62$	0.196152	0.0249114
$63$	−2.46410	−0.310448
$64$	1.00000	0.125000
$65$	−4.00000	−0.496139
$66$	−2.53590	−0.312148
$67$	−4.53590	−0.554148	−0.277074	−	0.960849i	$-0.589365\pi$
$67$	−4.53590	−0.554148	−0.277074	+	0.960849i	$0.589365\pi$
$68$	−0.732051	−0.0887742
$69$	0.732051	0.0881286
$70$	2.73205	0.326543
$71$	8.39230	0.995983	0.497992	−	0.867182i	$-0.334071\pi$
$71$	8.39230	0.995983	0.497992	+	0.867182i	$0.334071\pi$
$72$	−2.46410	−0.290397
$73$	−7.46410	−0.873607	−0.436804	−	0.899557i	$-0.643889\pi$
$73$	−7.46410	−0.873607	−0.436804	+	0.899557i	$0.643889\pi$
$74$	0.535898	0.0622969
$75$	1.80385	0.208290
$76$	−2.00000	−0.229416
$77$	−3.46410	−0.394771
$78$	−1.07180	−0.121357
$79$	0.928203	0.104431	0.0522155	−	0.998636i	$-0.483372\pi$
$79$	0.928203	0.104431	0.0522155	+	0.998636i	$0.483372\pi$
$80$	2.73205	0.305453
$81$	4.46410	0.496011
$82$	−2.00000	−0.220863
$83$	−6.39230	−0.701647	−0.350823	−	0.936442i	$-0.614098\pi$
$83$	−6.39230	−0.701647	−0.350823	+	0.936442i	$0.614098\pi$
$84$	0.732051	0.0798733
$85$	−2.00000	−0.216930
$86$	0	0
$87$	5.85641	0.627873
$88$	−3.46410	−0.369274
$89$	14.1962	1.50479	0.752395	−	0.658713i	$-0.228899\pi$
$89$	14.1962	1.50479	0.752395	+	0.658713i	$0.228899\pi$
$90$	−6.73205	−0.709620
$91$	−1.46410	−0.153480
$92$	1.00000	0.104257
$93$	0.143594	0.0148900
$94$	−8.19615	−0.845369
$95$	−5.46410	−0.560605
$96$	0.732051	0.0747146
$97$	−8.73205	−0.886605	−0.443303	−	0.896372i	$-0.646193\pi$
$97$	−8.73205	−0.886605	−0.443303	+	0.896372i	$0.646193\pi$
$98$	1.00000	0.101015
$99$	8.53590	0.857890
$100$	2.46410	0.246410
$101$	−1.46410	−0.145684	−0.0728418	−	0.997344i	$-0.523207\pi$
$101$	−1.46410	−0.145684	−0.0728418	+	0.997344i	$0.523207\pi$
$102$	−0.535898	−0.0530618
$103$	16.0000	1.57653	0.788263	−	0.615338i	$-0.210980\pi$
$103$	16.0000	1.57653	0.788263	+	0.615338i	$0.210980\pi$
$104$	−1.46410	−0.143567
$105$	2.00000	0.195180
$106$	3.46410	0.336463
$107$	6.92820	0.669775	0.334887	−	0.942258i	$-0.391302\pi$
$107$	6.92820	0.669775	0.334887	+	0.942258i	$0.391302\pi$
$108$	−4.00000	−0.384900
$109$	−8.92820	−0.855167	−0.427583	−	0.903976i	$-0.640635\pi$
$109$	−8.92820	−0.855167	−0.427583	+	0.903976i	$0.640635\pi$
$110$	−9.46410	−0.902367
$111$	0.392305	0.0372359
$112$	1.00000	0.0944911
$113$	19.4641	1.83103	0.915514	−	0.402285i	$-0.131784\pi$
$113$	19.4641	1.83103	0.915514	+	0.402285i	$0.131784\pi$
$114$	−1.46410	−0.137126
$115$	2.73205	0.254765
$116$	8.00000	0.742781
$117$	3.60770	0.333532
$118$	−11.6603	−1.07341
$119$	−0.732051	−0.0671070
$120$	2.00000	0.182574
$121$	1.00000	0.0909091
$122$	8.19615	0.742045
$123$	−1.46410	−0.132014
$124$	0.196152	0.0176150
$125$	−6.92820	−0.619677
$126$	−2.46410	−0.219520
$127$	−15.3205	−1.35948	−0.679738	−	0.733455i	$-0.737906\pi$
$127$	−15.3205	−1.35948	−0.679738	+	0.733455i	$0.737906\pi$
$128$	1.00000	0.0883883
$129$	0	0
$130$	−4.00000	−0.350823
$131$	−3.26795	−0.285522	−0.142761	−	0.989757i	$-0.545598\pi$
$131$	−3.26795	−0.285522	−0.142761	+	0.989757i	$0.545598\pi$
$132$	−2.53590	−0.220722
$133$	−2.00000	−0.173422
$134$	−4.53590	−0.391842
$135$	−10.9282	−0.940550
$136$	−0.732051	−0.0627728
$137$	17.3205	1.47979	0.739895	−	0.672722i	$-0.234875\pi$
$137$	17.3205	1.47979	0.739895	+	0.672722i	$0.234875\pi$
$138$	0.732051	0.0623163
$139$	−1.80385	−0.153000	−0.0765002	−	0.997070i	$-0.524375\pi$
$139$	−1.80385	−0.153000	−0.0765002	+	0.997070i	$0.524375\pi$
$140$	2.73205	0.230900
$141$	−6.00000	−0.505291
$142$	8.39230	0.704267
$143$	5.07180	0.424125
$144$	−2.46410	−0.205342
$145$	21.8564	1.81508
$146$	−7.46410	−0.617733
$147$	0.732051	0.0603785
$148$	0.535898	0.0440506
$149$	22.7846	1.86659	0.933294	−	0.359113i	$-0.116921\pi$
$149$	22.7846	1.86659	0.933294	+	0.359113i	$0.116921\pi$
$150$	1.80385	0.147284
$151$	−17.4641	−1.42121	−0.710604	−	0.703592i	$-0.751578\pi$
$151$	−17.4641	−1.42121	−0.710604	+	0.703592i	$0.751578\pi$
$152$	−2.00000	−0.162221
$153$	1.80385	0.145832
$154$	−3.46410	−0.279145
$155$	0.535898	0.0430444
$156$	−1.07180	−0.0858124
$157$	−8.19615	−0.654124	−0.327062	−	0.945003i	$-0.606059\pi$
$157$	−8.19615	−0.654124	−0.327062	+	0.945003i	$0.606059\pi$
$158$	0.928203	0.0738439
$159$	2.53590	0.201110
$160$	2.73205	0.215988
$161$	1.00000	0.0788110
$162$	4.46410	0.350733
$163$	12.3923	0.970640	0.485320	−	0.874337i	$-0.338703\pi$
$163$	12.3923	0.970640	0.485320	+	0.874337i	$0.338703\pi$
$164$	−2.00000	−0.156174
$165$	−6.92820	−0.539360
$166$	−6.39230	−0.496139
$167$	22.0526	1.70648	0.853239	−	0.521520i	$-0.174635\pi$
$167$	22.0526	1.70648	0.853239	+	0.521520i	$0.174635\pi$
$168$	0.732051	0.0564789
$169$	−10.8564	−0.835108
$170$	−2.00000	−0.153393
$171$	4.92820	0.376869
$172$	0	0
$173$	6.92820	0.526742	0.263371	−	0.964695i	$-0.415166\pi$
$173$	6.92820	0.526742	0.263371	+	0.964695i	$0.415166\pi$
$174$	5.85641	0.443973
$175$	2.46410	0.186269
$176$	−3.46410	−0.261116
$177$	−8.53590	−0.641597
$178$	14.1962	1.06405
$179$	−13.8564	−1.03568	−0.517838	−	0.855479i	$-0.673263\pi$
$179$	−13.8564	−1.03568	−0.517838	+	0.855479i	$0.673263\pi$
$180$	−6.73205	−0.501777
$181$	14.0526	1.04452	0.522259	−	0.852787i	$-0.325089\pi$
$181$	14.0526	1.04452	0.522259	+	0.852787i	$0.325089\pi$
$182$	−1.46410	−0.108526
$183$	6.00000	0.443533
$184$	1.00000	0.0737210
$185$	1.46410	0.107643
$186$	0.143594	0.0105288
$187$	2.53590	0.185443
$188$	−8.19615	−0.597766
$189$	−4.00000	−0.290957
$190$	−5.46410	−0.396408
$191$	16.0000	1.15772	0.578860	−	0.815427i	$-0.303498\pi$
$191$	16.0000	1.15772	0.578860	+	0.815427i	$0.303498\pi$
$192$	0.732051	0.0528312
$193$	4.92820	0.354740	0.177370	−	0.984144i	$-0.443241\pi$
$193$	4.92820	0.354740	0.177370	+	0.984144i	$0.443241\pi$
$194$	−8.73205	−0.626925
$195$	−2.92820	−0.209693
$196$	1.00000	0.0714286
$197$	8.92820	0.636108	0.318054	−	0.948073i	$-0.396971\pi$
$197$	8.92820	0.636108	0.318054	+	0.948073i	$0.396971\pi$
$198$	8.53590	0.606620
$199$	−24.7846	−1.75693	−0.878467	−	0.477803i	$-0.841433\pi$
$199$	−24.7846	−1.75693	−0.878467	+	0.477803i	$0.841433\pi$
$200$	2.46410	0.174238
$201$	−3.32051	−0.234211
$202$	−1.46410	−0.103014
$203$	8.00000	0.561490
$204$	−0.535898	−0.0375204
$205$	−5.46410	−0.381629
$206$	16.0000	1.11477
$207$	−2.46410	−0.171267
$208$	−1.46410	−0.101517
$209$	6.92820	0.479234
$210$	2.00000	0.138013
$211$	27.7128	1.90783	0.953914	−	0.300079i	$-0.0970130\pi$
$211$	27.7128	1.90783	0.953914	+	0.300079i	$0.0970130\pi$
$212$	3.46410	0.237915
$213$	6.14359	0.420952
$214$	6.92820	0.473602
$215$	0	0
$216$	−4.00000	−0.272166
$217$	0.196152	0.0133157
$218$	−8.92820	−0.604694
$219$	−5.46410	−0.369230
$220$	−9.46410	−0.638070
$221$	1.07180	0.0720969
$222$	0.392305	0.0263298
$223$	−21.2679	−1.42421	−0.712104	−	0.702074i	$-0.752257\pi$
$223$	−21.2679	−1.42421	−0.712104	+	0.702074i	$0.752257\pi$
$224$	1.00000	0.0668153
$225$	−6.07180	−0.404786
$226$	19.4641	1.29473
$227$	−0.928203	−0.0616070	−0.0308035	−	0.999525i	$-0.509807\pi$
$227$	−0.928203	−0.0616070	−0.0308035	+	0.999525i	$0.509807\pi$
$228$	−1.46410	−0.0969625
$229$	0.196152	0.0129621	0.00648106	−	0.999979i	$-0.497937\pi$
$229$	0.196152	0.0129621	0.00648106	+	0.999979i	$0.497937\pi$
$230$	2.73205	0.180146
$231$	−2.53590	−0.166850
$232$	8.00000	0.525226
$233$	16.3923	1.07390	0.536948	−	0.843615i	$-0.319577\pi$
$233$	16.3923	1.07390	0.536948	+	0.843615i	$0.319577\pi$
$234$	3.60770	0.235842
$235$	−22.3923	−1.46071
$236$	−11.6603	−0.759018
$237$	0.679492	0.0441377
$238$	−0.732051	−0.0474518
$239$	−4.39230	−0.284115	−0.142057	−	0.989858i	$-0.545372\pi$
$239$	−4.39230	−0.284115	−0.142057	+	0.989858i	$0.545372\pi$
$240$	2.00000	0.129099
$241$	21.1244	1.36074	0.680370	−	0.732869i	$-0.261819\pi$
$241$	21.1244	1.36074	0.680370	+	0.732869i	$0.261819\pi$
$242$	1.00000	0.0642824
$243$	15.2679	0.979439
$244$	8.19615	0.524705
$245$	2.73205	0.174544
$246$	−1.46410	−0.0933477
$247$	2.92820	0.186317
$248$	0.196152	0.0124557
$249$	−4.67949	−0.296551
$250$	−6.92820	−0.438178
$251$	−7.85641	−0.495892	−0.247946	−	0.968774i	$-0.579756\pi$
$251$	−7.85641	−0.495892	−0.247946	+	0.968774i	$0.579756\pi$
$252$	−2.46410	−0.155224
$253$	−3.46410	−0.217786
$254$	−15.3205	−0.961294
$255$	−1.46410	−0.0916856
$256$	1.00000	0.0625000
$257$	−23.8564	−1.48812	−0.744061	−	0.668112i	$-0.767103\pi$
$257$	−23.8564	−1.48812	−0.744061	+	0.668112i	$0.767103\pi$
$258$	0	0
$259$	0.535898	0.0332991
$260$	−4.00000	−0.248069
$261$	−19.7128	−1.22019
$262$	−3.26795	−0.201895
$263$	−8.92820	−0.550537	−0.275268	−	0.961367i	$-0.588767\pi$
$263$	−8.92820	−0.550537	−0.275268	+	0.961367i	$0.588767\pi$
$264$	−2.53590	−0.156074
$265$	9.46410	0.581375
$266$	−2.00000	−0.122628
$267$	10.3923	0.635999
$268$	−4.53590	−0.277074
$269$	1.85641	0.113187	0.0565935	−	0.998397i	$-0.481976\pi$
$269$	1.85641	0.113187	0.0565935	+	0.998397i	$0.481976\pi$
$270$	−10.9282	−0.665069
$271$	−10.7321	−0.651926	−0.325963	−	0.945383i	$-0.605688\pi$
$271$	−10.7321	−0.651926	−0.325963	+	0.945383i	$0.605688\pi$
$272$	−0.732051	−0.0443871
$273$	−1.07180	−0.0648681
$274$	17.3205	1.04637
$275$	−8.53590	−0.514734
$276$	0.732051	0.0440643
$277$	−8.00000	−0.480673	−0.240337	−	0.970690i	$-0.577258\pi$
$277$	−8.00000	−0.480673	−0.240337	+	0.970690i	$0.577258\pi$
$278$	−1.80385	−0.108188
$279$	−0.483340	−0.0289368
$280$	2.73205	0.163271
$281$	−19.4641	−1.16113	−0.580565	−	0.814214i	$-0.697168\pi$
$281$	−19.4641	−1.16113	−0.580565	+	0.814214i	$0.697168\pi$
$282$	−6.00000	−0.357295
$283$	11.0718	0.658150	0.329075	−	0.944304i	$-0.393263\pi$
$283$	11.0718	0.658150	0.329075	+	0.944304i	$0.393263\pi$
$284$	8.39230	0.497992
$285$	−4.00000	−0.236940
$286$	5.07180	0.299902
$287$	−2.00000	−0.118056
$288$	−2.46410	−0.145199
$289$	−16.4641	−0.968477
$290$	21.8564	1.28345
$291$	−6.39230	−0.374724
$292$	−7.46410	−0.436804
$293$	26.7321	1.56170	0.780852	−	0.624717i	$-0.214786\pi$
$293$	26.7321	1.56170	0.780852	+	0.624717i	$0.214786\pi$
$294$	0.732051	0.0426941
$295$	−31.8564	−1.85475
$296$	0.535898	0.0311485
$297$	13.8564	0.804030
$298$	22.7846	1.31988
$299$	−1.46410	−0.0846712
$300$	1.80385	0.104145
$301$	0	0
$302$	−17.4641	−1.00495
$303$	−1.07180	−0.0615731
$304$	−2.00000	−0.114708
$305$	22.3923	1.28218
$306$	1.80385	0.103119
$307$	8.05256	0.459584	0.229792	−	0.973240i	$-0.426195\pi$
$307$	8.05256	0.459584	0.229792	+	0.973240i	$0.426195\pi$
$308$	−3.46410	−0.197386
$309$	11.7128	0.666319
$310$	0.535898	0.0304370
$311$	−21.2679	−1.20599	−0.602997	−	0.797743i	$-0.706027\pi$
$311$	−21.2679	−1.20599	−0.602997	+	0.797743i	$0.706027\pi$
$312$	−1.07180	−0.0606785
$313$	5.12436	0.289646	0.144823	−	0.989458i	$-0.453739\pi$
$313$	5.12436	0.289646	0.144823	+	0.989458i	$0.453739\pi$
$314$	−8.19615	−0.462536
$315$	−6.73205	−0.379308
$316$	0.928203	0.0522155
$317$	−29.8564	−1.67690	−0.838451	−	0.544976i	$-0.816539\pi$
$317$	−29.8564	−1.67690	−0.838451	+	0.544976i	$0.816539\pi$
$318$	2.53590	0.142206
$319$	−27.7128	−1.55162
$320$	2.73205	0.152726
$321$	5.07180	0.283080
$322$	1.00000	0.0557278
$323$	1.46410	0.0814648
$324$	4.46410	0.248006
$325$	−3.60770	−0.200119
$326$	12.3923	0.686346
$327$	−6.53590	−0.361436
$328$	−2.00000	−0.110432
$329$	−8.19615	−0.451869
$330$	−6.92820	−0.381385
$331$	−0.392305	−0.0215630	−0.0107815	−	0.999942i	$-0.503432\pi$
$331$	−0.392305	−0.0215630	−0.0107815	+	0.999942i	$0.503432\pi$
$332$	−6.39230	−0.350823
$333$	−1.32051	−0.0723634
$334$	22.0526	1.20666
$335$	−12.3923	−0.677064
$336$	0.732051	0.0399366
$337$	−31.8564	−1.73533	−0.867665	−	0.497150i	$-0.834380\pi$
$337$	−31.8564	−1.73533	−0.867665	+	0.497150i	$0.834380\pi$
$338$	−10.8564	−0.590511
$339$	14.2487	0.773884
$340$	−2.00000	−0.108465
$341$	−0.679492	−0.0367966
$342$	4.92820	0.266487
$343$	1.00000	0.0539949
$344$	0	0
$345$	2.00000	0.107676
$346$	6.92820	0.372463
$347$	33.4641	1.79645	0.898224	−	0.439539i	$-0.144858\pi$
$347$	33.4641	1.79645	0.898224	+	0.439539i	$0.144858\pi$
$348$	5.85641	0.313936
$349$	−28.7846	−1.54080	−0.770402	−	0.637558i	$-0.779945\pi$
$349$	−28.7846	−1.54080	−0.770402	+	0.637558i	$0.779945\pi$
$350$	2.46410	0.131712
$351$	5.85641	0.312592
$352$	−3.46410	−0.184637
$353$	26.3923	1.40472	0.702360	−	0.711822i	$-0.252130\pi$
$353$	26.3923	1.40472	0.702360	+	0.711822i	$0.252130\pi$
$354$	−8.53590	−0.453678
$355$	22.9282	1.21690
$356$	14.1962	0.752395
$357$	−0.535898	−0.0283628
$358$	−13.8564	−0.732334
$359$	−0.928203	−0.0489887	−0.0244943	−	0.999700i	$-0.507798\pi$
$359$	−0.928203	−0.0489887	−0.0244943	+	0.999700i	$0.507798\pi$
$360$	−6.73205	−0.354810
$361$	−15.0000	−0.789474
$362$	14.0526	0.738586
$363$	0.732051	0.0384227
$364$	−1.46410	−0.0767398
$365$	−20.3923	−1.06738
$366$	6.00000	0.313625
$367$	−26.2487	−1.37017	−0.685086	−	0.728462i	$-0.740235\pi$
$367$	−26.2487	−1.37017	−0.685086	+	0.728462i	$0.740235\pi$
$368$	1.00000	0.0521286
$369$	4.92820	0.256552
$370$	1.46410	0.0761150
$371$	3.46410	0.179847
$372$	0.143594	0.00744498
$373$	8.92820	0.462285	0.231142	−	0.972920i	$-0.425754\pi$
$373$	8.92820	0.462285	0.231142	+	0.972920i	$0.425754\pi$
$374$	2.53590	0.131128
$375$	−5.07180	−0.261906
$376$	−8.19615	−0.422684
$377$	−11.7128	−0.603241
$378$	−4.00000	−0.205738
$379$	−0.535898	−0.0275273	−0.0137636	−	0.999905i	$-0.504381\pi$
$379$	−0.535898	−0.0275273	−0.0137636	+	0.999905i	$0.504381\pi$
$380$	−5.46410	−0.280302
$381$	−11.2154	−0.574582
$382$	16.0000	0.818631
$383$	−18.5359	−0.947140	−0.473570	−	0.880756i	$-0.657035\pi$
$383$	−18.5359	−0.947140	−0.473570	+	0.880756i	$0.657035\pi$
$384$	0.732051	0.0373573
$385$	−9.46410	−0.482335
$386$	4.92820	0.250839
$387$	0	0
$388$	−8.73205	−0.443303
$389$	7.07180	0.358554	0.179277	−	0.983799i	$-0.442624\pi$
$389$	7.07180	0.358554	0.179277	+	0.983799i	$0.442624\pi$
$390$	−2.92820	−0.148275
$391$	−0.732051	−0.0370214
$392$	1.00000	0.0505076
$393$	−2.39230	−0.120676
$394$	8.92820	0.449796
$395$	2.53590	0.127595
$396$	8.53590	0.428945
$397$	−31.3205	−1.57193	−0.785966	−	0.618270i	$-0.787834\pi$
$397$	−31.3205	−1.57193	−0.785966	+	0.618270i	$0.787834\pi$
$398$	−24.7846	−1.24234
$399$	−1.46410	−0.0732968
$400$	2.46410	0.123205
$401$	−29.7128	−1.48379	−0.741894	−	0.670518i	$-0.766072\pi$
$401$	−29.7128	−1.48379	−0.741894	+	0.670518i	$0.766072\pi$
$402$	−3.32051	−0.165612
$403$	−0.287187	−0.0143058
$404$	−1.46410	−0.0728418
$405$	12.1962	0.606032
$406$	8.00000	0.397033
$407$	−1.85641	−0.0920187
$408$	−0.535898	−0.0265309
$409$	7.46410	0.369076	0.184538	−	0.982825i	$-0.440921\pi$
$409$	7.46410	0.369076	0.184538	+	0.982825i	$0.440921\pi$
$410$	−5.46410	−0.269853
$411$	12.6795	0.625433
$412$	16.0000	0.788263
$413$	−11.6603	−0.573764
$414$	−2.46410	−0.121104
$415$	−17.4641	−0.857279
$416$	−1.46410	−0.0717835
$417$	−1.32051	−0.0646656
$418$	6.92820	0.338869
$419$	−11.0718	−0.540893	−0.270446	−	0.962735i	$-0.587171\pi$
$419$	−11.0718	−0.540893	−0.270446	+	0.962735i	$0.587171\pi$
$420$	2.00000	0.0975900
$421$	32.5359	1.58570	0.792851	−	0.609415i	$-0.208596\pi$
$421$	32.5359	1.58570	0.792851	+	0.609415i	$0.208596\pi$
$422$	27.7128	1.34904
$423$	20.1962	0.981971
$424$	3.46410	0.168232
$425$	−1.80385	−0.0874995
$426$	6.14359	0.297658
$427$	8.19615	0.396640
$428$	6.92820	0.334887
$429$	3.71281	0.179256
$430$	0	0
$431$	27.7128	1.33488	0.667440	−	0.744664i	$-0.267390\pi$
$431$	27.7128	1.33488	0.667440	+	0.744664i	$0.267390\pi$
$432$	−4.00000	−0.192450
$433$	1.41154	0.0678344	0.0339172	−	0.999425i	$-0.489202\pi$
$433$	1.41154	0.0678344	0.0339172	+	0.999425i	$0.489202\pi$
$434$	0.196152	0.00941562
$435$	16.0000	0.767141
$436$	−8.92820	−0.427583
$437$	−2.00000	−0.0956730
$438$	−5.46410	−0.261085
$439$	18.7321	0.894032	0.447016	−	0.894526i	$-0.352487\pi$
$439$	18.7321	0.894032	0.447016	+	0.894526i	$0.352487\pi$
$440$	−9.46410	−0.451183
$441$	−2.46410	−0.117338
$442$	1.07180	0.0509802
$443$	34.9282	1.65949	0.829745	−	0.558143i	$-0.188486\pi$
$443$	34.9282	1.65949	0.829745	+	0.558143i	$0.188486\pi$
$444$	0.392305	0.0186180
$445$	38.7846	1.83857
$446$	−21.2679	−1.00707
$447$	16.6795	0.788913
$448$	1.00000	0.0472456
$449$	−23.3205	−1.10056	−0.550281	−	0.834979i	$-0.685480\pi$
$449$	−23.3205	−1.10056	−0.550281	+	0.834979i	$0.685480\pi$
$450$	−6.07180	−0.286227
$451$	6.92820	0.326236
$452$	19.4641	0.915514
$453$	−12.7846	−0.600673
$454$	−0.928203	−0.0435627
$455$	−4.00000	−0.187523
$456$	−1.46410	−0.0685628
$457$	−6.39230	−0.299019	−0.149510	−	0.988760i	$-0.547770\pi$
$457$	−6.39230	−0.299019	−0.149510	+	0.988760i	$0.547770\pi$
$458$	0.196152	0.00916560
$459$	2.92820	0.136677
$460$	2.73205	0.127383
$461$	35.7128	1.66331	0.831656	−	0.555292i	$-0.187393\pi$
$461$	35.7128	1.66331	0.831656	+	0.555292i	$0.187393\pi$
$462$	−2.53590	−0.117981
$463$	10.9282	0.507877	0.253938	−	0.967220i	$-0.418274\pi$
$463$	10.9282	0.507877	0.253938	+	0.967220i	$0.418274\pi$
$464$	8.00000	0.371391
$465$	0.392305	0.0181927
$466$	16.3923	0.759359
$467$	23.8564	1.10394	0.551971	−	0.833863i	$-0.313876\pi$
$467$	23.8564	1.10394	0.551971	+	0.833863i	$0.313876\pi$
$468$	3.60770	0.166766
$469$	−4.53590	−0.209448
$470$	−22.3923	−1.03288
$471$	−6.00000	−0.276465
$472$	−11.6603	−0.536707
$473$	0	0
$474$	0.679492	0.0312101
$475$	−4.92820	−0.226121
$476$	−0.732051	−0.0335535
$477$	−8.53590	−0.390832
$478$	−4.39230	−0.200899
$479$	9.07180	0.414501	0.207250	−	0.978288i	$-0.433548\pi$
$479$	9.07180	0.414501	0.207250	+	0.978288i	$0.433548\pi$
$480$	2.00000	0.0912871
$481$	−0.784610	−0.0357751
$482$	21.1244	0.962188
$483$	0.732051	0.0333095
$484$	1.00000	0.0454545
$485$	−23.8564	−1.08326
$486$	15.2679	0.692568
$487$	8.78461	0.398069	0.199034	−	0.979993i	$-0.436219\pi$
$487$	8.78461	0.398069	0.199034	+	0.979993i	$0.436219\pi$
$488$	8.19615	0.371022
$489$	9.07180	0.410241
$490$	2.73205	0.123421
$491$	12.7846	0.576961	0.288481	−	0.957486i	$-0.406850\pi$
$491$	12.7846	0.576961	0.288481	+	0.957486i	$0.406850\pi$
$492$	−1.46410	−0.0660068
$493$	−5.85641	−0.263759
$494$	2.92820	0.131746
$495$	23.3205	1.04818
$496$	0.196152	0.00880750
$497$	8.39230	0.376446
$498$	−4.67949	−0.209693
$499$	−1.85641	−0.0831042	−0.0415521	−	0.999136i	$-0.513230\pi$
$499$	−1.85641	−0.0831042	−0.0415521	+	0.999136i	$0.513230\pi$
$500$	−6.92820	−0.309839
$501$	16.1436	0.721243
$502$	−7.85641	−0.350649
$503$	42.6410	1.90127	0.950634	−	0.310313i	$-0.100434\pi$
$503$	42.6410	1.90127	0.950634	+	0.310313i	$0.100434\pi$
$504$	−2.46410	−0.109760
$505$	−4.00000	−0.177998
$506$	−3.46410	−0.153998
$507$	−7.94744	−0.352958
$508$	−15.3205	−0.679738
$509$	−40.0000	−1.77297	−0.886484	−	0.462758i	$-0.846860\pi$
$509$	−40.0000	−1.77297	−0.886484	+	0.462758i	$0.846860\pi$
$510$	−1.46410	−0.0648315
$511$	−7.46410	−0.330192
$512$	1.00000	0.0441942
$513$	8.00000	0.353209
$514$	−23.8564	−1.05226
$515$	43.7128	1.92622
$516$	0	0
$517$	28.3923	1.24869
$518$	0.535898	0.0235460
$519$	5.07180	0.222627
$520$	−4.00000	−0.175412
$521$	−11.6603	−0.510845	−0.255423	−	0.966830i	$-0.582215\pi$
$521$	−11.6603	−0.510845	−0.255423	+	0.966830i	$0.582215\pi$
$522$	−19.7128	−0.862806
$523$	−12.9282	−0.565311	−0.282655	−	0.959222i	$-0.591215\pi$
$523$	−12.9282	−0.565311	−0.282655	+	0.959222i	$0.591215\pi$
$524$	−3.26795	−0.142761
$525$	1.80385	0.0787264
$526$	−8.92820	−0.389288
$527$	−0.143594	−0.00625503
$528$	−2.53590	−0.110361
$529$	1.00000	0.0434783
$530$	9.46410	0.411094
$531$	28.7321	1.24686
$532$	−2.00000	−0.0867110
$533$	2.92820	0.126835
$534$	10.3923	0.449719
$535$	18.9282	0.818338
$536$	−4.53590	−0.195921
$537$	−10.1436	−0.437728
$538$	1.85641	0.0800354
$539$	−3.46410	−0.149209
$540$	−10.9282	−0.470275
$541$	−8.00000	−0.343947	−0.171973	−	0.985102i	$-0.555014\pi$
$541$	−8.00000	−0.343947	−0.171973	+	0.985102i	$0.555014\pi$
$542$	−10.7321	−0.460981
$543$	10.2872	0.441465
$544$	−0.732051	−0.0313864
$545$	−24.3923	−1.04485
$546$	−1.07180	−0.0458687
$547$	44.3923	1.89808	0.949039	−	0.315159i	$-0.102058\pi$
$547$	44.3923	1.89808	0.949039	+	0.315159i	$0.102058\pi$
$548$	17.3205	0.739895
$549$	−20.1962	−0.861951
$550$	−8.53590	−0.363972
$551$	−16.0000	−0.681623
$552$	0.732051	0.0311582
$553$	0.928203	0.0394712
$554$	−8.00000	−0.339887
$555$	1.07180	0.0454952
$556$	−1.80385	−0.0765002
$557$	−31.8564	−1.34980	−0.674900	−	0.737910i	$-0.735813\pi$
$557$	−31.8564	−1.34980	−0.674900	+	0.737910i	$0.735813\pi$
$558$	−0.483340	−0.0204614
$559$	0	0
$560$	2.73205	0.115450
$561$	1.85641	0.0783775
$562$	−19.4641	−0.821044
$563$	−21.7128	−0.915086	−0.457543	−	0.889188i	$-0.651270\pi$
$563$	−21.7128	−0.915086	−0.457543	+	0.889188i	$0.651270\pi$
$564$	−6.00000	−0.252646
$565$	53.1769	2.23717
$566$	11.0718	0.465382
$567$	4.46410	0.187475
$568$	8.39230	0.352133
$569$	−19.8564	−0.832424	−0.416212	−	0.909268i	$-0.636643\pi$
$569$	−19.8564	−0.832424	−0.416212	+	0.909268i	$0.636643\pi$
$570$	−4.00000	−0.167542
$571$	13.0718	0.547038	0.273519	−	0.961867i	$-0.411812\pi$
$571$	13.0718	0.547038	0.273519	+	0.961867i	$0.411812\pi$
$572$	5.07180	0.212062
$573$	11.7128	0.489310
$574$	−2.00000	−0.0834784
$575$	2.46410	0.102760
$576$	−2.46410	−0.102671
$577$	17.3205	0.721062	0.360531	−	0.932747i	$-0.382595\pi$
$577$	17.3205	0.721062	0.360531	+	0.932747i	$0.382595\pi$
$578$	−16.4641	−0.684816
$579$	3.60770	0.149931
$580$	21.8564	0.907538
$581$	−6.39230	−0.265197
$582$	−6.39230	−0.264970
$583$	−12.0000	−0.496989
$584$	−7.46410	−0.308867
$585$	9.85641	0.407512
$586$	26.7321	1.10429
$587$	19.2679	0.795273	0.397637	−	0.917543i	$-0.369830\pi$
$587$	19.2679	0.795273	0.397637	+	0.917543i	$0.369830\pi$
$588$	0.732051	0.0301893
$589$	−0.392305	−0.0161646
$590$	−31.8564	−1.31151
$591$	6.53590	0.268851
$592$	0.535898	0.0220253
$593$	−26.7846	−1.09991	−0.549956	−	0.835194i	$-0.685356\pi$
$593$	−26.7846	−1.09991	−0.549956	+	0.835194i	$0.685356\pi$
$594$	13.8564	0.568535
$595$	−2.00000	−0.0819920
$596$	22.7846	0.933294
$597$	−18.1436	−0.742568
$598$	−1.46410	−0.0598716
$599$	−20.7846	−0.849236	−0.424618	−	0.905373i	$-0.639592\pi$
$599$	−20.7846	−0.849236	−0.424618	+	0.905373i	$0.639592\pi$
$600$	1.80385	0.0736418
$601$	−7.46410	−0.304467	−0.152234	−	0.988345i	$-0.548647\pi$
$601$	−7.46410	−0.304467	−0.152234	+	0.988345i	$0.548647\pi$
$602$	0	0
$603$	11.1769	0.455159
$604$	−17.4641	−0.710604
$605$	2.73205	0.111074
$606$	−1.07180	−0.0435388
$607$	−20.1962	−0.819737	−0.409868	−	0.912145i	$-0.634425\pi$
$607$	−20.1962	−0.819737	−0.409868	+	0.912145i	$0.634425\pi$
$608$	−2.00000	−0.0811107
$609$	5.85641	0.237314
$610$	22.3923	0.906638
$611$	12.0000	0.485468
$612$	1.80385	0.0729162
$613$	2.78461	0.112469	0.0562347	−	0.998418i	$-0.482091\pi$
$613$	2.78461	0.112469	0.0562347	+	0.998418i	$0.482091\pi$
$614$	8.05256	0.324975
$615$	−4.00000	−0.161296
$616$	−3.46410	−0.139573
$617$	−33.7128	−1.35723	−0.678613	−	0.734496i	$-0.737419\pi$
$617$	−33.7128	−1.35723	−0.678613	+	0.734496i	$0.737419\pi$
$618$	11.7128	0.471158
$619$	−16.2487	−0.653091	−0.326545	−	0.945182i	$-0.605885\pi$
$619$	−16.2487	−0.653091	−0.326545	+	0.945182i	$0.605885\pi$
$620$	0.535898	0.0215222
$621$	−4.00000	−0.160514
$622$	−21.2679	−0.852767
$623$	14.1962	0.568757
$624$	−1.07180	−0.0429062
$625$	−31.2487	−1.24995
$626$	5.12436	0.204810
$627$	5.07180	0.202548
$628$	−8.19615	−0.327062
$629$	−0.392305	−0.0156422
$630$	−6.73205	−0.268211
$631$	−10.7846	−0.429329	−0.214664	−	0.976688i	$-0.568866\pi$
$631$	−10.7846	−0.429329	−0.214664	+	0.976688i	$0.568866\pi$
$632$	0.928203	0.0369219
$633$	20.2872	0.806343
$634$	−29.8564	−1.18575
$635$	−41.8564	−1.66102
$636$	2.53590	0.100555
$637$	−1.46410	−0.0580098
$638$	−27.7128	−1.09716
$639$	−20.6795	−0.818068
$640$	2.73205	0.107994
$641$	−9.71281	−0.383633	−0.191817	−	0.981431i	$-0.561438\pi$
$641$	−9.71281	−0.383633	−0.191817	+	0.981431i	$0.561438\pi$
$642$	5.07180	0.200168
$643$	1.21539	0.0479303	0.0239652	−	0.999713i	$-0.492371\pi$
$643$	1.21539	0.0479303	0.0239652	+	0.999713i	$0.492371\pi$
$644$	1.00000	0.0394055
$645$	0	0
$646$	1.46410	0.0576043
$647$	−35.5167	−1.39630	−0.698152	−	0.715950i	$-0.745994\pi$
$647$	−35.5167	−1.39630	−0.698152	+	0.715950i	$0.745994\pi$
$648$	4.46410	0.175366
$649$	40.3923	1.58554
$650$	−3.60770	−0.141505
$651$	0.143594	0.00562787
$652$	12.3923	0.485320
$653$	29.7128	1.16275	0.581376	−	0.813635i	$-0.302515\pi$
$653$	29.7128	1.16275	0.581376	+	0.813635i	$0.302515\pi$
$654$	−6.53590	−0.255574
$655$	−8.92820	−0.348854
$656$	−2.00000	−0.0780869
$657$	18.3923	0.717552
$658$	−8.19615	−0.319519
$659$	−35.7128	−1.39117	−0.695587	−	0.718442i	$-0.744856\pi$
$659$	−35.7128	−1.39117	−0.695587	+	0.718442i	$0.744856\pi$
$660$	−6.92820	−0.269680
$661$	−30.4449	−1.18417	−0.592084	−	0.805876i	$-0.701695\pi$
$661$	−30.4449	−1.18417	−0.592084	+	0.805876i	$0.701695\pi$
$662$	−0.392305	−0.0152474
$663$	0.784610	0.0304717
$664$	−6.39230	−0.248070
$665$	−5.46410	−0.211889
$666$	−1.32051	−0.0511686
$667$	8.00000	0.309761
$668$	22.0526	0.853239
$669$	−15.5692	−0.601941
$670$	−12.3923	−0.478757
$671$	−28.3923	−1.09607
$672$	0.732051	0.0282395
$673$	3.32051	0.127996	0.0639981	−	0.997950i	$-0.479615\pi$
$673$	3.32051	0.127996	0.0639981	+	0.997950i	$0.479615\pi$
$674$	−31.8564	−1.22706
$675$	−9.85641	−0.379373
$676$	−10.8564	−0.417554
$677$	−35.8038	−1.37605	−0.688027	−	0.725685i	$-0.741523\pi$
$677$	−35.8038	−1.37605	−0.688027	+	0.725685i	$0.741523\pi$
$678$	14.2487	0.547218
$679$	−8.73205	−0.335105
$680$	−2.00000	−0.0766965
$681$	−0.679492	−0.0260382
$682$	−0.679492	−0.0260191
$683$	10.9282	0.418156	0.209078	−	0.977899i	$-0.432954\pi$
$683$	10.9282	0.418156	0.209078	+	0.977899i	$0.432954\pi$
$684$	4.92820	0.188435
$685$	47.3205	1.80802
$686$	1.00000	0.0381802
$687$	0.143594	0.00547844
$688$	0	0
$689$	−5.07180	−0.193220
$690$	2.00000	0.0761387
$691$	−8.73205	−0.332183	−0.166091	−	0.986110i	$-0.553115\pi$
$691$	−8.73205	−0.332183	−0.166091	+	0.986110i	$0.553115\pi$
$692$	6.92820	0.263371
$693$	8.53590	0.324252
$694$	33.4641	1.27028
$695$	−4.92820	−0.186937
$696$	5.85641	0.221987
$697$	1.46410	0.0554568
$698$	−28.7846	−1.08951
$699$	12.0000	0.453882
$700$	2.46410	0.0931343
$701$	−3.75129	−0.141684	−0.0708421	−	0.997488i	$-0.522569\pi$
$701$	−3.75129	−0.141684	−0.0708421	+	0.997488i	$0.522569\pi$
$702$	5.85641	0.221036
$703$	−1.07180	−0.0404236
$704$	−3.46410	−0.130558
$705$	−16.3923	−0.617370
$706$	26.3923	0.993287
$707$	−1.46410	−0.0550632
$708$	−8.53590	−0.320799
$709$	−0.535898	−0.0201261	−0.0100630	−	0.999949i	$-0.503203\pi$
$709$	−0.535898	−0.0201261	−0.0100630	+	0.999949i	$0.503203\pi$
$710$	22.9282	0.860480
$711$	−2.28719	−0.0857762
$712$	14.1962	0.532023
$713$	0.196152	0.00734597
$714$	−0.535898	−0.0200555
$715$	13.8564	0.518200
$716$	−13.8564	−0.517838
$717$	−3.21539	−0.120081
$718$	−0.928203	−0.0346402
$719$	−15.8038	−0.589384	−0.294692	−	0.955592i	$-0.595217\pi$
$719$	−15.8038	−0.589384	−0.294692	+	0.955592i	$0.595217\pi$
$720$	−6.73205	−0.250889
$721$	16.0000	0.595871
$722$	−15.0000	−0.558242
$723$	15.4641	0.575116
$724$	14.0526	0.522259
$725$	19.7128	0.732115
$726$	0.732051	0.0271690
$727$	−33.0718	−1.22657	−0.613283	−	0.789864i	$-0.710151\pi$
$727$	−33.0718	−1.22657	−0.613283	+	0.789864i	$0.710151\pi$
$728$	−1.46410	−0.0542632
$729$	−2.21539	−0.0820515
$730$	−20.3923	−0.754753
$731$	0	0
$732$	6.00000	0.221766
$733$	13.6603	0.504553	0.252276	−	0.967655i	$-0.418821\pi$
$733$	13.6603	0.504553	0.252276	+	0.967655i	$0.418821\pi$
$734$	−26.2487	−0.968858
$735$	2.00000	0.0737711
$736$	1.00000	0.0368605
$737$	15.7128	0.578789
$738$	4.92820	0.181410
$739$	−19.3205	−0.710716	−0.355358	−	0.934730i	$-0.615641\pi$
$739$	−19.3205	−0.710716	−0.355358	+	0.934730i	$0.615641\pi$
$740$	1.46410	0.0538214
$741$	2.14359	0.0787469
$742$	3.46410	0.127171
$743$	−12.9282	−0.474290	−0.237145	−	0.971474i	$-0.576212\pi$
$743$	−12.9282	−0.474290	−0.237145	+	0.971474i	$0.576212\pi$
$744$	0.143594	0.00526439
$745$	62.2487	2.28062
$746$	8.92820	0.326885
$747$	15.7513	0.576310
$748$	2.53590	0.0927216
$749$	6.92820	0.253151
$750$	−5.07180	−0.185196
$751$	48.6410	1.77494	0.887468	−	0.460869i	$-0.152462\pi$
$751$	48.6410	1.77494	0.887468	+	0.460869i	$0.152462\pi$
$752$	−8.19615	−0.298883
$753$	−5.75129	−0.209589
$754$	−11.7128	−0.426555
$755$	−47.7128	−1.73645
$756$	−4.00000	−0.145479
$757$	5.21539	0.189557	0.0947783	−	0.995498i	$-0.469786\pi$
$757$	5.21539	0.189557	0.0947783	+	0.995498i	$0.469786\pi$
$758$	−0.535898	−0.0194647
$759$	−2.53590	−0.0920473
$760$	−5.46410	−0.198204
$761$	−41.3205	−1.49787	−0.748934	−	0.662645i	$-0.769434\pi$
$761$	−41.3205	−1.49787	−0.748934	+	0.662645i	$0.769434\pi$
$762$	−11.2154	−0.406291
$763$	−8.92820	−0.323223
$764$	16.0000	0.578860
$765$	4.92820	0.178180
$766$	−18.5359	−0.669729
$767$	17.0718	0.616427
$768$	0.732051	0.0264156
$769$	21.1244	0.761764	0.380882	−	0.924624i	$-0.375620\pi$
$769$	21.1244	0.761764	0.380882	+	0.924624i	$0.375620\pi$
$770$	−9.46410	−0.341063
$771$	−17.4641	−0.628954
$772$	4.92820	0.177370
$773$	9.66025	0.347455	0.173728	−	0.984794i	$-0.444419\pi$
$773$	9.66025	0.347455	0.173728	+	0.984794i	$0.444419\pi$
$774$	0	0
$775$	0.483340	0.0173621
$776$	−8.73205	−0.313462
$777$	0.392305	0.0140739
$778$	7.07180	0.253536
$779$	4.00000	0.143315
$780$	−2.92820	−0.104846
$781$	−29.0718	−1.04027
$782$	−0.732051	−0.0261781
$783$	−32.0000	−1.14359
$784$	1.00000	0.0357143
$785$	−22.3923	−0.799216
$786$	−2.39230	−0.0853307
$787$	16.2487	0.579204	0.289602	−	0.957147i	$-0.406477\pi$
$787$	16.2487	0.579204	0.289602	+	0.957147i	$0.406477\pi$
$788$	8.92820	0.318054
$789$	−6.53590	−0.232684
$790$	2.53590	0.0902232
$791$	19.4641	0.692064
$792$	8.53590	0.303310
$793$	−12.0000	−0.426132
$794$	−31.3205	−1.11152
$795$	6.92820	0.245718
$796$	−24.7846	−0.878467
$797$	49.7654	1.76278	0.881390	−	0.472389i	$-0.156608\pi$
$797$	49.7654	1.76278	0.881390	+	0.472389i	$0.156608\pi$
$798$	−1.46410	−0.0518286
$799$	6.00000	0.212265
$800$	2.46410	0.0871191
$801$	−34.9808	−1.23598
$802$	−29.7128	−1.04920
$803$	25.8564	0.912453
$804$	−3.32051	−0.117105
$805$	2.73205	0.0962921
$806$	−0.287187	−0.0101157
$807$	1.35898	0.0478385
$808$	−1.46410	−0.0515069
$809$	−30.7846	−1.08233	−0.541165	−	0.840917i	$-0.682016\pi$
$809$	−30.7846	−1.08233	−0.541165	+	0.840917i	$0.682016\pi$
$810$	12.1962	0.428529
$811$	−49.9090	−1.75254	−0.876270	−	0.481820i	$-0.839976\pi$
$811$	−49.9090	−1.75254	−0.876270	+	0.481820i	$0.839976\pi$
$812$	8.00000	0.280745
$813$	−7.85641	−0.275536
$814$	−1.85641	−0.0650670
$815$	33.8564	1.18594
$816$	−0.535898	−0.0187602
$817$	0	0
$818$	7.46410	0.260976
$819$	3.60770	0.126063
$820$	−5.46410	−0.190815
$821$	−0.287187	−0.0100229	−0.00501145	−	0.999987i	$-0.501595\pi$
$821$	−0.287187	−0.0100229	−0.00501145	+	0.999987i	$0.501595\pi$
$822$	12.6795	0.442248
$823$	25.4641	0.887623	0.443811	−	0.896120i	$-0.353626\pi$
$823$	25.4641	0.887623	0.443811	+	0.896120i	$0.353626\pi$
$824$	16.0000	0.557386
$825$	−6.24871	−0.217552
$826$	−11.6603	−0.405712
$827$	9.85641	0.342741	0.171370	−	0.985207i	$-0.445181\pi$
$827$	9.85641	0.342741	0.171370	+	0.985207i	$0.445181\pi$
$828$	−2.46410	−0.0856335
$829$	−14.9282	−0.518478	−0.259239	−	0.965813i	$-0.583472\pi$
$829$	−14.9282	−0.518478	−0.259239	+	0.965813i	$0.583472\pi$
$830$	−17.4641	−0.606188
$831$	−5.85641	−0.203156
$832$	−1.46410	−0.0507586
$833$	−0.732051	−0.0253641
$834$	−1.32051	−0.0457255
$835$	60.2487	2.08499
$836$	6.92820	0.239617
$837$	−0.784610	−0.0271201
$838$	−11.0718	−0.382469
$839$	15.3205	0.528923	0.264461	−	0.964396i	$-0.414806\pi$
$839$	15.3205	0.528923	0.264461	+	0.964396i	$0.414806\pi$
$840$	2.00000	0.0690066
$841$	35.0000	1.20690
$842$	32.5359	1.12126
$843$	−14.2487	−0.490752
$844$	27.7128	0.953914
$845$	−29.6603	−1.02034
$846$	20.1962	0.694358
$847$	1.00000	0.0343604
$848$	3.46410	0.118958
$849$	8.10512	0.278167
$850$	−1.80385	−0.0618715
$851$	0.535898	0.0183704
$852$	6.14359	0.210476
$853$	2.53590	0.0868275	0.0434138	−	0.999057i	$-0.486177\pi$
$853$	2.53590	0.0868275	0.0434138	+	0.999057i	$0.486177\pi$
$854$	8.19615	0.280467
$855$	13.4641	0.460463
$856$	6.92820	0.236801
$857$	52.9282	1.80799	0.903996	−	0.427540i	$-0.140620\pi$
$857$	52.9282	1.80799	0.903996	+	0.427540i	$0.140620\pi$
$858$	3.71281	0.126753
$859$	1.12436	0.0383625	0.0191813	−	0.999816i	$-0.493894\pi$
$859$	1.12436	0.0383625	0.0191813	+	0.999816i	$0.493894\pi$
$860$	0	0
$861$	−1.46410	−0.0498964
$862$	27.7128	0.943902
$863$	21.4641	0.730647	0.365323	−	0.930881i	$-0.380958\pi$
$863$	21.4641	0.730647	0.365323	+	0.930881i	$0.380958\pi$
$864$	−4.00000	−0.136083
$865$	18.9282	0.643578
$866$	1.41154	0.0479662
$867$	−12.0526	−0.409326
$868$	0.196152	0.00665785
$869$	−3.21539	−0.109075
$870$	16.0000	0.542451
$871$	6.64102	0.225022
$872$	−8.92820	−0.302347
$873$	21.5167	0.728229
$874$	−2.00000	−0.0676510
$875$	−6.92820	−0.234216
$876$	−5.46410	−0.184615
$877$	50.9282	1.71972	0.859862	−	0.510527i	$-0.170550\pi$
$877$	50.9282	1.71972	0.859862	+	0.510527i	$0.170550\pi$
$878$	18.7321	0.632176
$879$	19.5692	0.660053
$880$	−9.46410	−0.319035
$881$	−36.3397	−1.22432	−0.612159	−	0.790735i	$-0.709699\pi$
$881$	−36.3397	−1.22432	−0.612159	+	0.790735i	$0.709699\pi$
$882$	−2.46410	−0.0829706
$883$	−40.0000	−1.34611	−0.673054	−	0.739594i	$-0.735018\pi$
$883$	−40.0000	−1.34611	−0.673054	+	0.739594i	$0.735018\pi$
$884$	1.07180	0.0360484
$885$	−23.3205	−0.783910
$886$	34.9282	1.17344
$887$	31.5167	1.05823	0.529113	−	0.848551i	$-0.322525\pi$
$887$	31.5167	1.05823	0.529113	+	0.848551i	$0.322525\pi$
$888$	0.392305	0.0131649
$889$	−15.3205	−0.513833
$890$	38.7846	1.30006
$891$	−15.4641	−0.518067
$892$	−21.2679	−0.712104
$893$	16.3923	0.548548
$894$	16.6795	0.557846
$895$	−37.8564	−1.26540
$896$	1.00000	0.0334077
$897$	−1.07180	−0.0357863
$898$	−23.3205	−0.778215
$899$	1.56922	0.0523364
$900$	−6.07180	−0.202393
$901$	−2.53590	−0.0844830
$902$	6.92820	0.230684
$903$	0	0
$904$	19.4641	0.647366
$905$	38.3923	1.27620
$906$	−12.7846	−0.424740
$907$	28.0000	0.929725	0.464862	−	0.885383i	$-0.346104\pi$
$907$	28.0000	0.929725	0.464862	+	0.885383i	$0.346104\pi$
$908$	−0.928203	−0.0308035
$909$	3.60770	0.119660
$910$	−4.00000	−0.132599
$911$	−20.9282	−0.693382	−0.346691	−	0.937979i	$-0.612695\pi$
$911$	−20.9282	−0.693382	−0.346691	+	0.937979i	$0.612695\pi$
$912$	−1.46410	−0.0484812
$913$	22.1436	0.732846
$914$	−6.39230	−0.211439
$915$	16.3923	0.541913
$916$	0.196152	0.00648106
$917$	−3.26795	−0.107917
$918$	2.92820	0.0966451
$919$	−8.14359	−0.268632	−0.134316	−	0.990939i	$-0.542884\pi$
$919$	−8.14359	−0.268632	−0.134316	+	0.990939i	$0.542884\pi$
$920$	2.73205	0.0900730
$921$	5.89488	0.194243
$922$	35.7128	1.17614
$923$	−12.2872	−0.404438
$924$	−2.53590	−0.0834249
$925$	1.32051	0.0434180
$926$	10.9282	0.359123
$927$	−39.4256	−1.29491
$928$	8.00000	0.262613
$929$	−11.8564	−0.388996	−0.194498	−	0.980903i	$-0.562308\pi$
$929$	−11.8564	−0.388996	−0.194498	+	0.980903i	$0.562308\pi$
$930$	0.392305	0.0128642
$931$	−2.00000	−0.0655474
$932$	16.3923	0.536948
$933$	−15.5692	−0.509713
$934$	23.8564	0.780605
$935$	6.92820	0.226576
$936$	3.60770	0.117921
$937$	−2.98076	−0.0973773	−0.0486886	−	0.998814i	$-0.515504\pi$
$937$	−2.98076	−0.0973773	−0.0486886	+	0.998814i	$0.515504\pi$
$938$	−4.53590	−0.148102
$939$	3.75129	0.122419
$940$	−22.3923	−0.730356
$941$	−45.3731	−1.47912	−0.739560	−	0.673091i	$-0.764966\pi$
$941$	−45.3731	−1.47912	−0.739560	+	0.673091i	$0.764966\pi$
$942$	−6.00000	−0.195491
$943$	−2.00000	−0.0651290
$944$	−11.6603	−0.379509
$945$	−10.9282	−0.355494
$946$	0	0
$947$	12.6795	0.412028	0.206014	−	0.978549i	$-0.433951\pi$
$947$	12.6795	0.412028	0.206014	+	0.978549i	$0.433951\pi$
$948$	0.679492	0.0220689
$949$	10.9282	0.354744
$950$	−4.92820	−0.159892
$951$	−21.8564	−0.708743
$952$	−0.732051	−0.0237259
$953$	−44.9282	−1.45537	−0.727684	−	0.685913i	$-0.759403\pi$
$953$	−44.9282	−1.45537	−0.727684	+	0.685913i	$0.759403\pi$
$954$	−8.53590	−0.276360
$955$	43.7128	1.41451
$956$	−4.39230	−0.142057
$957$	−20.2872	−0.655792
$958$	9.07180	0.293096
$959$	17.3205	0.559308
$960$	2.00000	0.0645497
$961$	−30.9615	−0.998759
$962$	−0.784610	−0.0252968
$963$	−17.0718	−0.550131
$964$	21.1244	0.680370
$965$	13.4641	0.433425
$966$	0.732051	0.0235533
$967$	−17.8564	−0.574223	−0.287112	−	0.957897i	$-0.592695\pi$
$967$	−17.8564	−0.574223	−0.287112	+	0.957897i	$0.592695\pi$
$968$	1.00000	0.0321412
$969$	1.07180	0.0344311
$970$	−23.8564	−0.765983
$971$	−34.1051	−1.09449	−0.547243	−	0.836974i	$-0.684323\pi$
$971$	−34.1051	−1.09449	−0.547243	+	0.836974i	$0.684323\pi$
$972$	15.2679	0.489720
$973$	−1.80385	−0.0578287
$974$	8.78461	0.281477
$975$	−2.64102	−0.0845802
$976$	8.19615	0.262352
$977$	−27.4641	−0.878654	−0.439327	−	0.898327i	$-0.644783\pi$
$977$	−27.4641	−0.878654	−0.439327	+	0.898327i	$0.644783\pi$
$978$	9.07180	0.290084
$979$	−49.1769	−1.57170
$980$	2.73205	0.0872722
$981$	22.0000	0.702406
$982$	12.7846	0.407973
$983$	−3.60770	−0.115068	−0.0575338	−	0.998344i	$-0.518324\pi$
$983$	−3.60770	−0.115068	−0.0575338	+	0.998344i	$0.518324\pi$
$984$	−1.46410	−0.0466739
$985$	24.3923	0.777203
$986$	−5.85641	−0.186506
$987$	−6.00000	−0.190982
$988$	2.92820	0.0931586
$989$	0	0
$990$	23.3205	0.741174
$991$	−26.5359	−0.842941	−0.421470	−	0.906842i	$-0.638486\pi$
$991$	−26.5359	−0.842941	−0.421470	+	0.906842i	$0.638486\pi$
$992$	0.196152	0.00622785
$993$	−0.287187	−0.00911361
$994$	8.39230	0.266188
$995$	−67.7128	−2.14664
$996$	−4.67949	−0.148275
$997$	3.21539	0.101832	0.0509162	−	0.998703i	$-0.483786\pi$
$997$	3.21539	0.101832	0.0509162	+	0.998703i	$0.483786\pi$
$998$	−1.85641	−0.0587635
$999$	−2.14359	−0.0678203

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	322.2.a.f.1.2	✓	2
3.2	odd	2		2898.2.a.w.1.1		2
4.3	odd	2		2576.2.a.u.1.1		2
5.4	even	2		8050.2.a.x.1.1		2
7.6	odd	2		2254.2.a.o.1.1		2
23.22	odd	2		7406.2.a.s.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
322.2.a.f.1.2	✓	2	1.1	even	1	trivial
2254.2.a.o.1.1		2	7.6	odd	2
2576.2.a.u.1.1		2	4.3	odd	2
2898.2.a.w.1.1		2	3.2	odd	2
7406.2.a.s.1.2		2	23.22	odd	2
8050.2.a.x.1.1		2	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 322 = 2 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	322.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.732051 q^{3} +1.00000 q^{4} +2.73205 q^{5} +0.732051 q^{6} +1.00000 q^{7} +1.00000 q^{8} -2.46410 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.732051 q^{3} +1.00000 q^{4} +2.73205 q^{5} +0.732051 q^{6} +1.00000 q^{7} +1.00000 q^{8} -2.46410 q^{9} +2.73205 q^{10} -3.46410 q^{11} +0.732051 q^{12} -1.46410 q^{13} +1.00000 q^{14} +2.00000 q^{15} +1.00000 q^{16} -0.732051 q^{17} -2.46410 q^{18} -2.00000 q^{19} +2.73205 q^{20} +0.732051 q^{21} -3.46410 q^{22} +1.00000 q^{23} +0.732051 q^{24} +2.46410 q^{25} -1.46410 q^{26} -4.00000 q^{27} +1.00000 q^{28} +8.00000 q^{29} +2.00000 q^{30} +0.196152 q^{31} +1.00000 q^{32} -2.53590 q^{33} -0.732051 q^{34} +2.73205 q^{35} -2.46410 q^{36} +0.535898 q^{37} -2.00000 q^{38} -1.07180 q^{39} +2.73205 q^{40} -2.00000 q^{41} +0.732051 q^{42} -3.46410 q^{44} -6.73205 q^{45} +1.00000 q^{46} -8.19615 q^{47} +0.732051 q^{48} +1.00000 q^{49} +2.46410 q^{50} -0.535898 q^{51} -1.46410 q^{52} +3.46410 q^{53} -4.00000 q^{54} -9.46410 q^{55} +1.00000 q^{56} -1.46410 q^{57} +8.00000 q^{58} -11.6603 q^{59} +2.00000 q^{60} +8.19615 q^{61} +0.196152 q^{62} -2.46410 q^{63} +1.00000 q^{64} -4.00000 q^{65} -2.53590 q^{66} -4.53590 q^{67} -0.732051 q^{68} +0.732051 q^{69} +2.73205 q^{70} +8.39230 q^{71} -2.46410 q^{72} -7.46410 q^{73} +0.535898 q^{74} +1.80385 q^{75} -2.00000 q^{76} -3.46410 q^{77} -1.07180 q^{78} +0.928203 q^{79} +2.73205 q^{80} +4.46410 q^{81} -2.00000 q^{82} -6.39230 q^{83} +0.732051 q^{84} -2.00000 q^{85} +5.85641 q^{87} -3.46410 q^{88} +14.1962 q^{89} -6.73205 q^{90} -1.46410 q^{91} +1.00000 q^{92} +0.143594 q^{93} -8.19615 q^{94} -5.46410 q^{95} +0.732051 q^{96} -8.73205 q^{97} +1.00000 q^{98} +8.53590 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{6} + 2 q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 - 2 * q^6 + 2 * q^7 + 2 * q^8 + 2 * q^9	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{6} + 2 q^{7} + 2 q^{8} + 2 q^{9} + 2 q^{10} - 2 q^{12} + 4 q^{13} + 2 q^{14} + 4 q^{15} + 2 q^{16} + 2 q^{17} + 2 q^{18} - 4 q^{19} + 2 q^{20} - 2 q^{21} + 2 q^{23} - 2 q^{24} - 2 q^{25} + 4 q^{26} - 8 q^{27} + 2 q^{28} + 16 q^{29} + 4 q^{30} - 10 q^{31} + 2 q^{32} - 12 q^{33} + 2 q^{34} + 2 q^{35} + 2 q^{36} + 8 q^{37} - 4 q^{38} - 16 q^{39} + 2 q^{40} - 4 q^{41} - 2 q^{42} - 10 q^{45} + 2 q^{46} - 6 q^{47} - 2 q^{48} + 2 q^{49} - 2 q^{50} - 8 q^{51} + 4 q^{52} - 8 q^{54} - 12 q^{55} + 2 q^{56} + 4 q^{57} + 16 q^{58} - 6 q^{59} + 4 q^{60} + 6 q^{61} - 10 q^{62} + 2 q^{63} + 2 q^{64} - 8 q^{65} - 12 q^{66} - 16 q^{67} + 2 q^{68} - 2 q^{69} + 2 q^{70} - 4 q^{71} + 2 q^{72} - 8 q^{73} + 8 q^{74} + 14 q^{75} - 4 q^{76} - 16 q^{78} - 12 q^{79} + 2 q^{80} + 2 q^{81} - 4 q^{82} + 8 q^{83} - 2 q^{84} - 4 q^{85} - 16 q^{87} + 18 q^{89} - 10 q^{90} + 4 q^{91} + 2 q^{92} + 28 q^{93} - 6 q^{94} - 4 q^{95} - 2 q^{96} - 14 q^{97} + 2 q^{98} + 24 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 - 2 * q^6 + 2 * q^7 + 2 * q^8 + 2 * q^9 + 2 * q^10 - 2 * q^12 + 4 * q^13 + 2 * q^14 + 4 * q^15 + 2 * q^16 + 2 * q^17 + 2 * q^18 - 4 * q^19 + 2 * q^20 - 2 * q^21 + 2 * q^23 - 2 * q^24 - 2 * q^25 + 4 * q^26 - 8 * q^27 + 2 * q^28 + 16 * q^29 + 4 * q^30 - 10 * q^31 + 2 * q^32 - 12 * q^33 + 2 * q^34 + 2 * q^35 + 2 * q^36 + 8 * q^37 - 4 * q^38 - 16 * q^39 + 2 * q^40 - 4 * q^41 - 2 * q^42 - 10 * q^45 + 2 * q^46 - 6 * q^47 - 2 * q^48 + 2 * q^49 - 2 * q^50 - 8 * q^51 + 4 * q^52 - 8 * q^54 - 12 * q^55 + 2 * q^56 + 4 * q^57 + 16 * q^58 - 6 * q^59 + 4 * q^60 + 6 * q^61 - 10 * q^62 + 2 * q^63 + 2 * q^64 - 8 * q^65 - 12 * q^66 - 16 * q^67 + 2 * q^68 - 2 * q^69 + 2 * q^70 - 4 * q^71 + 2 * q^72 - 8 * q^73 + 8 * q^74 + 14 * q^75 - 4 * q^76 - 16 * q^78 - 12 * q^79 + 2 * q^80 + 2 * q^81 - 4 * q^82 + 8 * q^83 - 2 * q^84 - 4 * q^85 - 16 * q^87 + 18 * q^89 - 10 * q^90 + 4 * q^91 + 2 * q^92 + 28 * q^93 - 6 * q^94 - 4 * q^95 - 2 * q^96 - 14 * q^97 + 2 * q^98 + 24 * q^99

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